How to not accidently kill one of my tenants?

[Account Closed]

Hello,

I am trying to put in a handrail on my 1st floor steps, but stuck on one thing.

The wall appears to be plaster, with 2 sheets of plasterboard roughly 3/4inch total. Behind that directly is a cinderblock wall.

No studs.

What screws do I use to handle this so that it can withstand 200lbs of downward and outward load?

I purchased these on the right, and the handrail kit included the back on the left. 

What is the way to do this so it's 100% safe to support weight?

Thank you for your time and knowledge.

-Dan